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3 years ago

When a linear function has a slope of 5, what is the "run" part of the slope?

Mathematics

1 answer:

alukav5142 [94]3 years ago

7 0

Slope equals rise over the run
so if slope = 5 then the rise also equals 5 and the run is 1

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2. In how many ways can 3 different novels, 2 different mathematics books and 5 different chemistry books be arranged on a books

insens350 [35]

The number of ways of the books can be arranged are illustrations of permutations.

When the books are arranged in any order, the number of arrangements is 3628800
When the mathematics book must not be together, the number of arrangements is 2903040
When the novels must be together, and the chemistry books must be together, the number of arrangements is 17280
When the mathematics books must be together, and the novels must not be together, the number of arrangements is 302400

The given parameters are:

$\mathbf{Novels = 3}$

$\mathbf{Mathematics = 2}$

$\mathbf{Chemistry = 5}$

(a) The books in any order

First, we calculate the total number of books

$\mathbf{n = Novels + Mathematics + Chemistry}$

$\mathbf{n = 3 + 2 + 5}$

$\mathbf{n = 10}$

The number of arrangement is n!:

So, we have:

$\mathbf{n! = 10!}$

$\mathbf{n! = 3628800}$

(b) The mathematics book, not together

There are 2 mathematics books.

If the mathematics books, must be together

The number of arrangements is:

$\mathbf{Maths\ together = 2 \times 9!}$

Using the complement rule, we have:

$\mathbf{Maths\ not\ together = Total - Maths\ together}$

This gives

$\mathbf{Maths\ not\ together = 3628800 - 2 \times 9!}$

$\mathbf{Maths\ not\ together = 2903040}$

(c) The novels must be together and the chemistry books, together

We have:

$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the novels in:

$\mathbf{Novels = 3!\ ways}$

Next, arrange the chemistry books in:

$\mathbf{Chemistry = 5!\ ways}$

Now, the 5 chemistry books will be taken as 1; the novels will also be taken as 1.

Literally, the number of books now is:

$\mathbf{n =Mathematics + 1 + 1}$

$\mathbf{n =2 + 1 + 1}$

$\mathbf{n =4}$

So, the number of arrangements is:

$\mathbf{Arrangements = n! \times 3! \times 5!}$

$\mathbf{Arrangements = 4! \times 3! \times 5!}$

$\mathbf{Arrangements = 17280}$

(d) The mathematics must be together and the chemistry books, not together

We have:

$\mathbf{Mathematics = 2}$

$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the mathematics in:

$\mathbf{Mathematics = 2!}$

Literally, the number of chemistry and mathematics now is:

$\mathbf{n =Chemistry + 1}$

$\mathbf{n =5 + 1}$

$\mathbf{n =6}$

So, the number of arrangements of these books is:

$\mathbf{Arrangements = n! \times 2!}$

$\mathbf{Arrangements = 6! \times 2!}$

Now, there are 7 spaces between the chemistry and mathematics books.

For the 3 novels not to be together, the number of arrangement is:

$\mathbf{Arrangements = ^7P_3}$

So, the total arrangement is:

$\mathbf{Total = 6! \times 2!\times ^7P_3}$

$\mathbf{Total = 6! \times 2!\times 210}$

$\mathbf{Total = 302400}$

Read more about permutations at:

brainly.com/question/1216161

8 0

3 years ago

Consider the quadratic function, f(x)=-2x^2+12x+32=0. Select all statements that are true for the function. The value of the dis

Andrews [41]

Answer:

Step-by-step explanation:

-2x² + 12x + 32 = 0

discriminant = 12² - 4(-2)(32) = 400

positive discriminant means there are two distinct real roots

x = [-12 ± √(12² – 4(-2)·32)] / [2·(-2)]

= [-12 ± √400] / (-4)

= [-12 ± 20] /(-4)

= 8, -2

8 0

3 years ago

Read 2 more answers

Theodore needs to mix a 10% fungicide solution with a 50% fungicide solution to create 100 milliliters of a 26% solution. How ma

solmaris [256]

Answer:

Therefore 40 milliliter of 50% fungicide solution is required

Therfore 60 milliliter of 10% fungicide solution is required

Step-by-step explanation:

i) Let the 10% fungicide solution have x milliliter and the 50% fungicide solution have y milliliter.

ii) Therefore 10x + 50y = 26(x + y)

x + y = 100

iii) form the first equation in ii) we get

16 x = 24 y Therefore $x = \frac{24}{16} y = \frac{3}{2} y$

iv) substituting the value obtained in iii) in the second equation in ii) we get

$\frac{3}{2} y + y = \frac{5}{2} y = 100$

Therefore y = 100 ÷ 2.5 = 40 milliliter

Therfore x = 100 - 40 = 60 milliliter

4 0

3 years ago

Am I on the right track?

alekssr [168]

if you want to be sure :/

7 0

4 years ago

There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter. To the nearest inch, how many inches are in 11 meter

Leno4ka [110]

Answer:

3937.01 Inch are in 100 meter

3 0

3 years ago